Chapter 2
Orifice Design
Abstract This chapter describes the main design specifications for orifice plates
(more precisely, orifice meters): it points the reader to important parts of ISO 5167
and gives reasons for the requirements in the standard. It covers the orifice plate (the
circularity of the bore, the flatness, the parallelism of the two faces, the surface
condition of the upstream face, and, above all, the edge sharpness), the pipe (the
pressure tappings, the pipe roughness, the effect of upstream steps, the concentricity
of the orifice plate in the pipe and the circularity and cylindricality of the pipe), the
measurements of both the orifice plate and the pipe, and the pressure loss. A very
significant incorrect installation of an orifice plate within the pipe, a reversed orifice
plate, is also covered. Appendix 2.A considers the use of orifice plates of diameter
smaller than that permitted in ISO 5167. The effect of upstream fittings is not
covered here: it is Chap. 8. The basic instruction remains to follow ISO 5167. For
some important deviations from ISO 5167 the errors in discharge coefficient can be
calculated using what is described in this chapter.
2.1 Introduction
An orifice plate is fundamentally a plate with a hole machined through it which is
inserted into a pipe. As flow passes through the hole it produces a pressure difference across the hole (some of which is recovered). The plate must be sufficiently
thin that over the range of permitted thickness its thickness does not affect the
discharge coefficient but thick enough not to be distorted by the forces imposed by
the pressure difference. The pressure difference is proportional to the square of the
flowrate (mass or volume).
The hole may be of any shape if the discharge coefficient is determined by
calibration. A few shapes and designs have been produced for which the discharge
coefficient can be predicted. Of these only for a round sharp-edged centrally located
hole are there sufficient data to allow prediction of flowrate with an uncertainty
which is low enough to use for trade in the most valuable fluids: only this shape is
covered in this book. Other shapes are listed in NOTE 1 of Chap. 1.
© Springer International Publishing Switzerland 2015
M. Reader-Harris, Orifice Plates and Venturi Tubes,
Experimental Fluid Mechanics, DOI 10.1007/978-3-319-16880-7_2
33
34
2 Orifice Design
The main design specifications are in ISO 5167-1:2003 and ISO 5167-2:2003
(ISO 2003a, b). This chapter points the reader to important parts of ISO 5167 and
gives reasons for the requirements in the standard. It covers the orifice plate (the
circularity of the bore, the flatness, the parallelism of the two faces, the surface
condition of the upstream face, and, above all, the edge sharpness), the pipe (the
pressure tappings, the pipe roughness, the effect of upstream steps, the concentricity
of the orifice plate in the pipe and the circularity and cylindricality of the pipe), the
measurements of both the orifice plate and the pipe, and the pressure loss. A very
significant incorrect installation of an orifice plate within the pipe, a reversed orifice
plate, is also covered. Appendix 2.A considers the use of orifice plates of diameter
smaller than that permitted in ISO 5167-2:2003. The installation of the orifice meter
(the orifice plate and pipe) in terms of upstream straight lengths, flow conditioners
and pulsations is covered in Chap. 8.
To design an orifice plate, given the range of mass flowrates, the density, the
desired range of differential pressures (discussed in Sect. 4.3), the discharge coefficient (from Chap. 5), the expansibility factor (from Chap. 6) and the desired pipe
diameter (D), the throat diameter (d) can be determined from Eq. 1.15:
Ce pd 2 pffiffiffiffiffiffiffiffiffiffiffiffiffi
qm ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi4
2q1 Dp:
1b 4
ð1:15Þ
If this gives too large a value of diameter ratio (β) (=d/D) then a larger value of D is
required (or a second orifice meter in parallel could be used). For best accuracy
0.2 ≤ β ≤ 0.6 is recommended. The uncertainty increases if β is outside this range. If
there is no preferred value of D then it would be good to choose a value of D so that
0.5 ≤ β ≤ 0.6. As β increases the effects of pipe roughness (see Sect. 2.3.3),
installation (see Chap. 8) and eccentricity (see Sect. 2.3.5) increase: this is reflected
in an increase in the uncertainty of the discharge-coefficient equation (see 5.3.3.1 of
ISO 5167-2:2003 and Fig. 5.12). As β is reduced the pressure loss increases. If
β < 0.2 there is a scarcity of data (see Chap. 5) and unless D is large there are
increasing problems with edge sharpness (see Sect. 2.2.4); there is an increase in the
uncertainty of the discharge coefficient.
2.2 Orifice Plate
2.2.1 General
The orifice plate is as in Fig. 2.1 (see also Fig. 2.2: the plate pictured is for insertion
between flanges and has a handle for ease of removal). Good quality of manufacture
is very important, especially the following:
• The circularity of the bore (5.1.8.3 of ISO 5167-2:2003) (see Sect. 2.4)
• the flatness (5.1.3.1 of ISO 5167-2:2003; see Sect. 2.2.2),
2.2 Orifice Plate
35
Fig. 2.1 Orifice plate
nomenclature
Fig. 2.2 An orifice plate
• the parallelism of the two faces (5.1.5.4 of ISO 5167-2:2003),
• the surface condition of the upstream face (5.1.3.2 of ISO 5167-2:2003; see
Sect. 2.2.3),
• and, above all, the edge sharpness (5.1.7.2 of ISO 5167-2:2003; see Sect. 2.2.4).
The requirement for parallelism is not, as far as the author knows, based on
experiment, but simply on what can reasonably be manufactured; that is why there
are different requirements for D < 200 mm. This lack of similarity suggests that the
requirement for larger orifice plates may be sufficient but not necessary. The
required values for the thicknesses of the orifice plate (E) and of the orifice bore
(e) are based on experiment (see Sect. 2.2.5).
36
2 Orifice Design
2.2.2 Flatness
The effect of buckling an orifice plate was measured by Jepson and Chipchase
(1973, 1975) who measured the effect of bending β = 0.2 and β = 0.7 plates in an 8″
line. The deflections of the orifice bore were in the range 0.0039D to
0.0625D [0.79 to 12.7 mm (1/32″ to ½″)]. An under-estimation of flow of up to
14 % was measured. The experimental work was compared with theoretical work in
which the effects of changing the bore position relative to the pressure tappings, of
changing the inward radial momentum of the fluid and of changing the bore size
were considered. The first was shown to be smaller than the other two and was
neglected. Quite good agreement between experiment and theory was obtained.
Work was also undertaken by Gorter (1978). Ting (1993) reported results with 4″
and 6″ orifice plates that had been bent by a press, and his results were compared
with the theory of Mason et al. (1975). The data are presented in Fig. 2.3. With a
slope of 1 % the theoretical model of Jepson and Chipchase shown gives a shift in
discharge coefficient of a little less than 0.2 % in absolute value at maximum.
The fundamental need is that the orifice plate not be bent in such a way as to cause
a significant shift in discharge coefficient. It can be bent both by poor manufacture
and by the effect of the differential pressure across it. The former can be measured in
the laboratory; the latter (except in the case of permanent distortion) cannot. It must
be calculated. The requirement on which ISO 5167-2:2003 is based is that the
discharge coefficient should not change by more than 0.2 % from the value given by
a flat plate perpendicular to the pipe axis (Norman et al. 1983). This corresponds to a
requirement that the plate should not have a slope (=2δ/(D − d)) greater than 1 %
(this assumes that the experimental data for β = 0.2 in Fig. 2.3 have quite high
16
% shift in discharge coefficient
14
12
Jepson and Chipchase: beta = 0.7
Jepson and Chipchase: beta = 0.2
theoretical: Jepson and Chipchase: beta = 0.7
theoretical: Jepson and Chipchase: beta = 0.2
Ting: beta = 0.5
theory: Mason et al.:beta = 0.5
10
8
D
6
δ
Flow
4
2
0
-2
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
Ratio of orifice plate deflection to pipe diameter (δ /D)
Fig. 2.3 The effect of bending an orifice plate: positive deflection (δ) is in the downstream
direction
2.2 Orifice Plate
37
uncertainty, but that the theoretical model of Jepson and Chipchase can be used). To
ensure this, the slope of the plate should not exceed 0.5 % when measured in the
laboratory and the differential pressure should not cause a slope of more than 0.5 %.
The slope in the laboratory can be measured using feeler gauges. Advice on how to
calculate the maximum differential pressure so that the orifice plate is neither elastically deformed beyond the permitted limit nor permanently buckled is given in
5.2.5.1.2.3 of ISO/TR 9464:2008 (ISO 2008). To carry out the calculation the
material of the plate, the thickness and how it is supported at the outside edge must
be known. More accurate predictions can be calculated using finite element analysis;
however, ISO/TR 9464 will normally provide adequate guidance.
2.2.3 Surface Condition of the Upstream Face of the Plate
The requirement (in 5.1.3.2 of ISO 5167-2:2003) on the roughness of the upstream
face of the orifice plate that Ra < 10−4d is normally fairly easy to meet at manufacture (definitions of Ra and k are given in Sect. 2.3.3.1). If it were exceeded it
would make it difficult to meet the edge-sharpness requirement. It appears to be
based on work of McVeigh (1962) and Dall (1958): McVeigh recommends that
k/d ≤ 3 × 10−4, which is equivalent to the ISO limit: some of McVeigh’s data were
taken in a 1″ pipe. Data were taken by Studzinski and Berg (1988), but these are
surprising: the effect of Ra = 2 μm is greater in an 8″ pipe than in a 4″ pipe.
Computational work by Reader-Harris (1991, 1993) concluded that the ISO limit is
reasonable for Red ≈ 107 and conservative for smaller Red. 2.4.1 of API MPMS
14.3.2 (API 2000) requires a maximum of 1.27 µm (50 μin.); this is sufficient (but
not non-dimensional); the plates used by API to provide data used to develop the
orifice discharge-coefficient equation had Ra in the range 0.10–0.53 µm (4–21 μin.).
One important cause of poor surface condition in practice is the presence of
contamination due to deposition. This is covered in 9.3 of ISO/TR 12767:2007
(ISO 2007c), which contains some examples of the effect of contamination
(Pritchard et al. 2003, 2004), but does not give a general formula for its effect. The
experiments by Pritchard et al. used grease on an orifice plate; this grease moved
during the test. Experiments on the effect of grease deposits on an orifice plate have
also been performed by Botros et al. (1992) and by Burgin (1971).
The importance of the final portion of the orifice plate approaching the sharp
edge can be seen from Morrison et al. (1990): the pressure on the front face of the
orifice changes very slowly near the corner between the orifice plate and the pipe,
but very rapidly over the portion of the face between a circle whose diameter is
about 1.1d and the sharp edge.
There are two patterns of contamination that may occur: one is contamination up
to the orifice edge, the other contamination in which a clean ring (kept clean by the
flow) is left. The first gives an error that is impossible to predict (it can be directly
measured), because the contamination changes the edge sharpness and has a
potentially very large effect; some examples of shifts in discharge coefficient are
38
2 Orifice Design
Fig. 2.4 A contaminated
orifice plate
given in Tables 5 and 6 of ISO/TR 12767:2007. The second has been analysed by
Reader-Harris et al. (2010): both computational and experimental work were carried
out with a uniform layer of contamination of thickness hc on the front face of an
orifice plate, starting a distance rc from the orifice edge, as shown in Fig. 2.4. The
key idea of using θ, the largest angle between the sharp edge and the contamination,
was due to Neil Barton at NEL.
The percentage shift, S, in discharge coefficient due to contamination of this
pattern was shown to be
S ¼ 22:8
1:4 4
hc
2rc
1
rc
Dð1 bÞ
ð2:1Þ
This has an uncertainty of 0.28 % based on 2 standard deviations (Reader-Harris
et al. 2010).
The effect of very small amounts of liquid in a gas flow can be similar to that of
contamination (Ting and Corpron 1995).
The effects of oil coating on orifice plates and pipes have been considered by
Johansen et al. (1966) and Johansen (1966). Generally coating the pipe has more
effect than coating the plate. Moreover, as would be expected, the effect of coating
the pipe increases rapidly with β (see also Morrow 1998). The discharge coefficient
increases, but the effect generally reduces with time as the flow removes the oil.
Botros et al. (1992) found that very thin liquid films reduce surface roughness and
thus the discharge coefficient, an effect not seen in Johansen’s or Morrow’s work.
The condition of the downstream face of the orifice plate is much less important
than that of the upstream (Hobbs and Humphreys 1990): when a plate was
roughened by sticking sandpaper of particle size about 1 mm to the downstream
face of orifice plates of diameter ratio 0.4, 0.6 and 0.75 in a 12″ line there was no
significant change in discharge coefficient; it did not matter whether the roughness
was over the whole of the downstream face or simply on the bevel.
In conclusion, contamination is the main cause of problems with surface condition: the main aim must be to avoid contamination. Where this is not possible,
there is one pattern of contamination where the error can be predicted from the
contamination adhering to the plate; in other situations the error needs to be directly
measured.
2.2 Orifice Plate
39
2.2.4 Edge Sharpness
A rounded orifice upstream edge leads to error because the flow remains attached to
the initial part of the rounded edge: therefore there is an increase in the area of the
vena contracta and thus in the discharge coefficient.
The edge sharpness of an orifice plate may be destroyed by erosion, cavitation or
poor handling.
This is a particularly critical area for small orifice plates. To achieve the required
sharpness in large plate sizes, i.e. d > 100 mm, is straightforward at manufacture,
although subsequent damage is possible. When d < 50 mm it is difficult, and for
d < 25 mm very difficult.
The effect of edge radius, i.e. the radius of the sharp edge, r, is a well-worked
area. It is discussed in Hobbs and Humphreys (1990). The effect is given in Fig. 2.5,
which shows their data, taken in 12″ pipe. The data points with the smallest value of
r/d for each β are taken as having no shift in discharge coefficient. The slope of the
fitted line is approximately 550; so the effect of a change of edge radius of
0.0002d on C is 0.11 %.
Data have also been taken in 2″ and 4″ pipe (Herning 1962), 6″ pipe (Herning
and Wolowski 1963), 3″ pipe (Crocket and Upp 1973) and 4″ pipe (Benedict et al.
1974). These are shown together with the NEL data in Fig. 1 of ISO/TR
12767:2007 (ISO 2007c). Data with r/d up to 0.025 were taken by Burgin (1971).
The effect of edge sharpness is also discussed in Spencer et al. (1969)
(see below).
1.6
% shift in discharge coefficient
1.4
beta = 0.75
beta = 0.6
1.2
beta = 0.4
limit in ISO 5167-2:2003
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020
Edge radius ratio: r/d
Fig. 2.5 Effect of orifice edge radius (r) on discharge coefficient: NEL tests
40
2 Orifice Design
Measurement techniques for edge radius are available including casting
(Gallagher 1968), lead foil impression (Crocket and Upp 1973), and an optical
method in which the condition of the orifice edge is determined by observing the
distortion caused by a fine beam of light falling onto the edge (Benedict et al. 1974):
the results are compared in Brain and Reid (1973).
Measurements of the edge radii of the plates used for the EEC data for the
discharge-coefficient equation are given in Spencer (1987): techniques for the same
plate included lead foil, casting and profilometry, in which a Talysurf or equivalent
machine is used: the typical spread of measurements of the same plate in different
laboratories was around ±5 to ±20 µm, based on the average value of edge radius
taken in a laboratory; the spread of measurements at different points of the circumference for a single plate in one laboratory could be as large as ±20 µm.
In almost all cases it is better to manufacture the edge sharpness at the required
value rather than to attempt to measure it and make appropriate corrections.
From this work comes the requirement that r ≤ 0.0004d, where r is the radius of
the edge. In practice the uncertainty of the measurement tends to be about 10 μm at
best. So for small d it may not be clear whether or not a plate has passed. Difficulties in measurement of edge radius led to difficulty in determining how the plates
with small diameters should be used in determining the orifice-plate dischargecoefficient equation. Certainly for d less than about 38 mm edge radius is a cause of
additional uncertainty. The fact that the plates in 3″ pipe gave data in agreement
with the data for larger sizes is more remarkable than that the plates in 2″ pipe did
not. It is common to look at an orifice upstream edge and to decide that it is
unacceptable if it reflects a beam of light when viewed without magnification. This
method enables some poor plates to be identified but takes no account of the fact
that the required edge sharpness is proportional to orifice diameter.
One possible solution for small orifices is to spark-erode them. The consequences of using this technique require more research, but it appears that one
manufacturer gave a consistent edge radius of about 9 μm. This gives sharp edges
for d ≥ 25 mm. This area is investigated in Appendix 2.A.
Another source of error is damage to an edge by a chip, nick or groove in the
sharp edge. It is helpful to distinguish between a notch that extends completely
through the orifice bore (increasing the orifice area) and a groove that cuts the
upstream face of the plate and the sharp edge but does not increase the orifice area.
The tests of Humphreys and Hobbs (1990) were of the latter type and gave
remarkably small effects even where a large amount of damage was inflicted on the
plate: for example, a cold chisel was held at an angle of 45° against the sharp edge
and struck with a hammer: the metal was not removed but displaced. After one
strike the dimensions of the damage were of the order of 2 mm for β = 0.34 and
3 mm for β = 0.75 in a 12″ line: the area of the bore was not increased; the increase
in discharge coefficient in the case of both plates was in the range 0.02 or 0.03 to
0.18 % depending on the location of the damage relative to the pressure tappings. A
further strike increased the damage to the order of 3 mm for β = 0.34 and 4 mm for
β = 0.75: then there was a decrease in discharge coefficient from that of the
undamaged plate of 0.33 % to 0.51 % for β = 0.34 and 0.10 % to 0.20 % for
2.2 Orifice Plate
41
β = 0.75 depending on the location of the damage relative to the pressure tappings.
Botros et al. (1992) undertook a study of the effect of both a groove and a notch.
The effect of a notch that extends through the plate is approximately 43 times the
effect of the area increase (and at maximum twice the area increase). Botros et al.
state that a typical small nick encountered in a pipeline system causes a measurement error of the order of −0.002 %.
In conclusion, the sharpness of the upstream edge of the orifice plate is of the
utmost importance to the accuracy of the flow measurement. In fiscal measurement
systems the orifice plate is checked regularly mainly because of the risk that its edge
might be damaged (the check will also find any contamination adhering to the
surface). A large defect on a small part of the sharp edge has a small effect on the
discharge coefficient, whereas a small defect over the whole of the sharp edge has a
large effect.
2.2.5 Plate Thickness E and Orifice (Bore) Thickness e
2.2.5.1 General
Essentially the plate thickness E has to be sufficiently large that the plate does not
bend significantly (see Sect. 2.2.2) but sufficiently small that the installation is
geometrically similar to those used for determining the orifice discharge-coefficient
equation (Chap. 5). The orifice (bore) thickness e has to be sufficiently small that
the orifice is essentially a thin plate but sufficiently large that a square edge can be
obtained. Where e < E the plate is bevelled.
The plate thickness is easy to measure with a micrometer caliper. Measuring the
orifice (bore) thickness using a depth micrometer is less accurate.
2.2.5.2 Plate Thickness E
Husain and Teyssandier (1986b) measured the shift in discharge coefficient in a 6″
flange-tapped orifice meter between a baseline with E = 3.2 mm (1/8″) and tests
with values of E up to 19 mm (3/4″). Throughout e was 2.8 mm (0.11″). Bevel
angles of 45° and 30° (to the pipe axis) were used. To do this the plate was initially
19 mm (¾″) thick and was successively machined thinner. Part of the effect of
changing the plate thickness E is to move downstream corner or flange tappings
relative to the upstream face of the plate: the difference in discharge coefficient
between an orifice plate of standard thickness with the downstream tapping
(E − 3.2 mm) downstream of the flange tapping and the baseline (which is an orifice
plate of standard thickness with flange tappings) was calculated from the ReaderHarris/Gallagher (1998) Equation (Eq. 5.22) [5.3.2.1 of ISO 5167-2:2003 (ISO
2003b)]; this is described in Fig. 2.6 as the simple model.
42
2 Orifice Design
0.3
% shift in discharge coefficient
0.2
0.1
0
-0.1
-0.2
beta = 0.3, bevel angle 45 deg
beta = 0.3, bevel angle 30 deg
beta = 0.5, bevel angle 45 deg
beta = 0.5, bevel angle 30 deg
beta = 0.7, bevel angle 45 deg
beta = 0.7, bevel angle 30 deg
Simple model: beta = 0.3
Simple model: beta = 0.5
Simple model: beta = 0.7
-0.3
-0.4
-0.5
-0.6
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
E/D
Fig. 2.6 Effect of changing E/D. In the simple model the shift is based on the location of the
downstream tapping relative to the downstream face of the baseline plate
In Fig. 2.6 the experimental data for β = 0.3 are surprisingly scattered; those for
β = 0.5 are in good agreement with the simple model; those for β = 0.7 show a
larger shift than the simple model, presumably because in the simple model there is
a flow in the part of the orifice meter which in the experiment is the downstream
part of the plate.
2.2.5.3 Orifice (Bore) Thickness e
The effect of increasing the orifice (bore) thickness e is to change the orifice from a
thin orifice, in which it is as if e were as close as possible to 0 given that a square
edge is required on the orifice, to a thick orifice, whose discharge coefficient is
around 0.8, because the flow has now reattached to the orifice bore. The discharge
coefficient changes slowly where e/d is small but more rapidly around e/d = 0.5.
This is well exhibited in a set of data from NBS (now NIST) (see Lansverk 1990)
given in Fig. 2.7. Flow is unstable where the flow reattaches intermittently to the
orifice bore.
In addition to the tests described in Sect. 2.2.5.2, Husain and Teyssandier (1986)
measured the shift in discharge coefficient using an unbevelled orifice plate in a 6″
flange-tapped orifice meter from a baseline with E = e = 3.2 mm (1/8″) to tests with
values of E (=e) up to 19 mm (3/4″). To do this the plate was initially 19 mm (¾″)
thick and was successively machined thinner. The data are shown in Fig. 2.8.
The famous OSU data (Beitler 1935) were collected by Ohio State University in
the 1930s on many plates, some used in more than one pipe. In some cases the plate
2.2 Orifice Plate
43
% shift in discharge coefficient
30
25
20
15
10
5
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
e/d
Fig. 2.7 Shift in discharge coefficient as a function of e/d: 4″ β = 0.25
% shift in discharge coefficient
8
Beitler (7585-T), beta = 0.12, D = 2 inch
Beitler (7567-T), beta = 0.18, D = 2 inch
Beitler (7567-T), beta = 0.23, D = 1.5 inch
Husain and Teyssandier, beta = 0.3, D = 6 inch
Beitler (7567-T), beta = 0.36, D = 1 inch
Husain and Teyssandier, beta = 0.5, D = 6 inch
Husain and Teyssandier, beta = 0.7, D = 6 inch
7
6
5
4
3
2
1
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
e/D
Fig. 2.8 Effect of changing e/D
was re-bevelled to change the value of e. Those for small pipe diameters are
presented in Reader-Harris et al. (2008). It is then possible using the points with
e/d < 0.09 as the baseline to plot the effect of e/D (see Fig. 2.8). A point from
Beitler (7585-T, β = 0.12, D = 2″, e/d = 0.125) was omitted because the spread of
the deviations from the Reader-Harris/Gallagher (RG) (API) Equation (Eq. 5.23)
for different Reynolds numbers was 1.39 %, more than three times the spread of the
44
2 Orifice Design
8
% shift in discharge coefficient
Husain and Teyssandier, beta = 0.3, D = 6 inch
7
Beitler (7585-T), beta = 0.12, D = 2 inch
Beitler (7567-T), beta = 0.18, D = 2 inch
6
Beitler (7567-T), beta = 0.23, D = 1.5 inch
Beitler (7567-T), beta = 0.36, D = 1 inch
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
e/d
Fig. 2.9 Effect of orifice (bore) thickness (e) for β < 0.4: shift in discharge coefficient from that
obtained when e/d < 0.09
deviations for any plotted points (except for the point from Beitler (7585-T),
β = 0.12, D = 2″, e/D = 0.0625). Where no points are available with e/d < 0.09 the
data are not plotted. For β ≥ 0.2 the ISO limit of e/D ≤ 0.02 is adequate, but for
smaller β it is inadequate. The data for β up to 0.4 are plotted in Fig. 2.9 against e/d:
a common curve for all data as a function of e/d is obtained. A new analysis of the
OSU data for larger β and for larger D could be undertaken: the conclusions of
Beitler (1935) are that there are two requirements: that e/d ≤ 0.125 and that
e/h′ ≤ 0.25, where h′ is the dam height, the distance from the sharp edge of the
orifice plate to the nearest point of the pipe wall (i.e. h′ = D(1 − β)/2). The
conclusions as regards requirements in Sect. 2.2.5.4 are more demanding than
Beitler’s and on the basis of the work here should prove adequate.
Husain and Goodson (1986) took data in 2″ pipes with plates that are on the
maximum limit in ISO 5167 for plate thickness or exceed it; these data show that an
unbevelled plate with E = 3.57 mm (5/32″) did not significantly change its discharge coefficient when it was machined to be an unbevelled plate with
E = 3.18 mm (1/8″) and then when it was bevelled with e = 0.79 mm. Larger shifts
would have been expected from Figs. 2.8 and 2.9.
2.2.5.4 Requirements
On the basis of the work in Sects. 2.2.5.2 and 2.2.5.3 the requirements in ISO 51672:2003 are reasonable:
2.2 Orifice Plate
45
0:005D e 0:02D:
e E 0:05D:
However, there is an additional requirement that should be included in the next
revision:
e 0:1d:
This last requirement is only additional to the previous requirements when β < 0.2.
The angle of bevel makes no difference to the discharge coefficient, provided
that it is 45° ± 15°. Husain and Goodson (1986) showed that having a 30° angle to
the bore gave the same discharge coefficient as having a 45° angle; they also state
that Ohio State data show that having a 60° angle to the bore makes a negligible
difference from having a 45° angle [only data with a 45° bevel are given in Beitler
(1935)].
If the plate is unbevelled (e = E), then provided that both faces meet the specification for the front face and that flange or corner tappings are used the plate can
be used bi-directionally. It will be fairly thin (E/D ≤ 0.02); so there may be issues
with plate bending.
2.2.6 Circularity
The circularity of the orifice plate (and that of the pipe) is considered in Sect. 2.4.
2.3 The Pipe
2.3.1 General
The orifice plate can only be used as a flowmeter in accordance with ISO 5167
when it has upstream and downstream pipe (for an example see Fig. 2.10).
In addition to the effect of upstream (and downstream) fittings, considered in
Chap. 8, it is necessary to consider
•
•
•
•
•
the location of the pressure tappings (Sect. 2.3.2),
the pipe roughness (Sect. 2.3.3),
the effect of upstream steps (Sect. 2.3.4),
the concentricity of the orifice plate in the pipe (Sect. 2.3.5)
and the circularity and cylindricality of the pipe (see Sect. 2.4).
46
2 Orifice Design
Fig. 2.10 Orifice plate held between flanges
2.3.2 Pressure Tappings
2.3.2.1 General
In ISO 5167 there are three choices for the tappings: flange tappings (Sect. 2.3.2.2),
D and D/2 tappings (Sect. 2.3.2.2) and corner tappings (Sect. 2.3.2.3): see Fig. 2.11.
2.3.2.2 Flange and D and D/2 Tappings
General
For fiscal oil and gas measurement flange tappings are normally specified: they are
located in the flanges 25.4 mm (1″) upstream of the upstream face of the plate and
25.4 mm (1″) downstream of the downstream face of the plate. This distance will
normally place them within the thickness of a flange holding the plate (see Fig. 2.12
for an example).
Flange tappings are generally the simplest in terms of manufacturing. Because of
the large difference between the inside and outside diameters of the flanges no
significant pressure expansion of the pipe will occur at the tappings and no correction in pipe diameter due to static pressure is required; moreover, the smaller the
flow velocity is at the tapping, the less important are the roundness, sharpness and
depth of the tappings (the main issues with tapping quality occur with Venturi tubes
or throat-tapped nozzles: see Chaps. 7 and 9). The disadvantage in the use of orifice
2.3 The Pipe
47
Fig. 2.11 Flow through an orifice plate, showing the pressure tapping positions and approximate
pressure profile
Fig. 2.12 8″ orifice meter
with flange tappings
plates with flange tappings is that because they are not geometrically similar they
introduce additional complexity to the discharge-coefficient equation; moreover,
they may be unsuitable for pipes smaller than those covered by ISO 5167-2:2003
(i.e. D < 50 mm) because the downstream tapping might be in the pressure-recovery
zone, which starts a little to the right of the vena contracta in Fig. 2.11.
48
2 Orifice Design
For D and D/2 tappings the tappings are located 1D upstream and D/2 downstream, both measured from the upstream face of the orifice plate: the upstream
tapping is upstream of any disturbance to the pressure from the plate; the downstream
tapping is near the pressure minimum for large β. Great care should be taken if
tappings are formed by welding a boss to a pipe wall that the welding heat does not
create an internal bulge which alters the local velocity at the tapping as well as altering
the pipe diameter at the tapping. Welding of bosses should be carried out prior to
machining a bore, or an alternative method of preventing distortion employed.
Tapping Diameter
For both flange and D and D/2 tappings the tapping diameter is not very critical as
long as the centre of the tapping is correctly located: in 5.2.2.7 of ISO 5167-2:2003
the diameter must be less than both 0.13D and 13 mm. In the equivalent API
standard, API MPMS 14.3.2 (API 2000), the tapping diameters must be 9.5 mm
(3/8″) for 2″ and 3″ pipes and 12.7 mm (1/2″) for 4″ pipes and larger. When the data
on which the discharge-coefficient equation is based were collected, all the European data were collected in tubes to ISO specification; the American data were
collected in tubes to API specification: for example, for 2″ tubes the European
tappings were generally 2 mm in diameter, i.e. 0.04D, and the American tappings
were 9.5 mm (3/8″) in diameter, i.e. 0.19D. There was no noticeable difference
between European data and American data: the mean deviation for European water
data from the Reader-Harris/Gallagher (1998) Equation was 0.005 %, for American
water data it was 0.008 %. All the 3″ data were American (with tappings 9.5 mm
(3/8″) in diameter, i.e. 0.122D) and 95 % of the 3″ data are within about 0.26 % of
the Reader-Harris/Gallagher (1998) Equation in ISO 5167-2:2003, an exceptionally
good result. So there was no sign that tapping diameter had much effect on the
discharge coefficient.
Tapping Location
The tolerances on location are given in 5.2.2.2 and 5.2.2.3 of ISO 5167-2:2003. The
permitted upstream and downstream spacings for flange tappings are:
25.4 mm ± 0.5 mm when β > 0.6 and D < 150 mm
25.4 mm ± 1 mm in all other cases, i.e. β ≤ 0.6, or β > 0.6, but
150 mm ≤ D ≤ 1000 mm
The Reader-Harris/Gallagher (1998) Equation (Eq. 5.22a, 5.22b) can be used to
calculate the effect of moving the tappings: the effect is shown in Figs. 2.13 and
2.14. In Eq. 5.22a, 5.22b A was taken as 0; this gives the maximum shift.
Work has also been carried out by Zedan and Teyssandier (1990).
From Figs. 2.13 and 2.14 the largest errors can occur for large β at the upstream
flange-tapping location.
2.3 The Pipe
49
0.07
0.06
D = 2 inch
D = 3 inch
D = 4 inch
D = 6 inch
D = 8 inch
% error
0.05
0.04
0.03
0.02
0.01
0.00
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
β
Fig. 2.13 Maximum absolute error due to permissible variation of ISO upstream flange-tapping
location
0.020
0.018
0.016
% error
0.014
0.012
0.010
0.008
D = 2 inch
D = 3 inch
D = 4 inch
D = 6 inch
D = 8 inch
0.006
0.004
0.002
0.000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
β
Fig. 2.14 Maximum absolute error due to permissible variation of ISO downstream flangetapping location
50
2 Orifice Design
Because the pressure profile is very flat both D upstream of the orifice plate and
near the vena contracta the effect of small errors in the location of D and D/2
tappings is very small.
2.3.2.3 Corner Tappings
Corner tappings are located in the corners between the plate and the pipe wall. They
may be either single tappings or annular slots. In 5.2.3.3 of ISO 5167-2:2003 the
three lines headed ‘For clean fluids and vapours’ give requirements for sizes of
corner tappings based on geometrical similarity to the original orifice runs on which
the discharge coefficient is based. As β increases the discharge coefficient changes
more rapidly with tapping position (as can be seen from the Reader-Harris/
Gallagher (1998) Equation) and so the orifice meters need to be closer to the
original ones. However, it was accepted that to require a tapping size of a maximum
of 1 mm was not sensible; so for D < 100 mm values up to 2 mm are acceptable
even if not permitted by instructions 1 or 2 in 5.2.3.3 of ISO 5167-2:2003. The
three lines headed ‘For any values of β′ give requirements based on what is sensible
for particular fluids. For certain fluids in certain sizes it is not possible to design a
system using single corner tappings that is compliant with ISO 5167.
Except for pipes smaller than those covered by ISO 5167-2:2003 flange tappings
are much more commonly used than corner tappings.
NOTE Corner tappings may be installed in a carrier ring: this is shown in Fig. 4 of
ISO 5167-2:2003. The permitted diameter of the carrier ring is given in 5.2.3.6 of
ISO 5167-2:2003. If the tappings are installed in a carrier ring then differences
between the ring diameter and that of the pipe become important: see 7.3 of ISO/TR
12767:2007.
2.3.2.4 Number of Tappings
Single tappings or multiple tappings in each tapping plane are permitted. If there are
4 tappings in each tapping plane, those in each tapping plane should be connected
in a triple-T arrangement as in Fig. 4.8. If there is an asymmetric flow profile the
triple-Ts reduce the effect of upstream installation. However, if there is any risk of
liquid in a gas flow tappings should only be in the top half of the pipe, and in
practice a single tapping on the side or on the top is common. If there is any risk of
gas in a liquid flow tappings should only be in the bottom half of the pipe. See Sect.
4.2.2 for more details.
See ISO 2186:2007 (ISO 2007a) for more information on steam measurement
with orifice plates.
2.3 The Pipe
51
2.3.3 Pipe Roughness
2.3.3.1 Uniform Roughness
New roughness limits for pipework upstream of orifice plates were included in ISO
5167-2:2003. These are derived from a physical understanding of the effect of pipe
roughness on orifice plate discharge coefficients and the knowledge of the roughness of the pipes on which the discharge-coefficient equation in ISO 5167-2:2003 is
based. The physical understanding was obtained from computational work at NEL
(Reader-Harris and Keegans 1986; Reader-Harris 1990). Pipe roughness limits have
been calculated to ensure that roughness will not shift the discharge coefficient from
that given by the discharge-coefficient equation by more than an appropriate fraction of its uncertainty.
The friction factor, λ, can be measured directly (see Sect. 1.5), using:
Dp ¼
kqu2 x
2D
ð1:19Þ
where Δp is the difference in pressure between two tappings spaced a distance
x apart in a pipe of diameter D and u is the mean velocity in the pipe. It is simpler to
measure the arithmetic mean deviation of the roughness profile, Ra, (the average of
the absolute values of the deviation from the mean), to deduce the uniform
equivalent roughness, k, by taking it to be approximately equal to πRa (based on the
assumption that the wall has a sinusoidal profile) and to calculate λ using the
Colebrook-White Equation (Schlichting 1960):
1
2k
18:7
pffiffiffi ¼ 1:74 2lg
pffiffiffi
þ
D ReD k
k
ð1:21Þ
(following ISO 80000-2:2009, log10 is written lg).
The arithmetic mean deviation of the roughness profile, Ra, or the friction factor,
λ, (or both) was measured for each of the pipes used to collect the data to which the
discharge-coefficient equation was fitted. Values of roughness are given in the
reports listed in Chap. 5. The API (US) pipes had rms (Rq) approximately 1–6 µm
(Ra values would be similar, probably slightly smaller) (Whetstone et al. 1989).
NOTE When the 24″ pipework (D = 585.95 mm) for the orifice equation tests was
made British Gas (Stewart 1989) measured both its Ra value, obtaining 4.2, 6.1, 5.5
and 3.3 μm at four locations along it, an average of 4.8 μm, and the pressure loss
along it, which gave a friction factor of 0.0095 at a Reynolds number of 2.8 × 107,
which corresponded to k = 13.8 μm. On this occasion k/Ra = 2.9, in good agreement
with expectation.
Using the measurements of pipe roughness it was possible to fit a dischargecoefficient equation containing an explicit friction factor term; this was done at the
time when the PR14 Equation (see Chap. 5) was developed and, using the PR14
52
2 Orifice Design
tapping terms, the following equation for the C∞ and slope terms was obtained for
ReD > 3700 (see Eq. 5.C.4):
C1 þ Cs ¼ 0:5945 þ 0:0157b1:3 0:2417b8 þ 0:000514ð106 b=ReD Þ0:7
þ ð3:134 þ 4:726A0 Þb3:5 k
ð2:2Þ
where
2100b 0:9
A0 ¼
:
ReD
This gives the change in discharge coefficient due to roughness, ΔCrough, as
DCrough ¼ 3:134b3:5 Dk
ð2:3Þ
provided that Red is sufficiently large that A′ is negligible. This equation was
evaluated by Morrow and Morrison (1999): ‘they compared the CFD results with
the Reader-Harris correlation. The changes in pipe roughness and Cd values were in
agreement with the equation predictions of Reader-Harris. They also found that the
new Reader-Harris equation compensates for systematic variations of Cd with the β
ratio that have been included in the past equations’ (Morrow et al. 2002).
Figure 2.15 gives measured and computed (using CFD) values of ΔC as a
function of β3.5Δλ. The computed values (Reader-Harris 1990) and the European
experimental data (Clark and Stephens 1957; Herning and Lugt 1958; Spencer et al.
1969; Thibessard 1960; Witte 1953) were obtained using corner tappings. The
North American experimental data (Bean and Murdock 1959; Brennan et al. 1989;
Studzinski et al. 1990) were obtained using flange tappings. In computational work
the effect of roughness on discharge coefficients obtained with different pairs of
pressure tappings was considered and it was shown that the effect of pipe roughness
on the discharge coefficient using D and D/2 tappings is about 25 % less than on
that using corner tappings. Since all the computational and most of the experimental
data in Fig. 2.15 were collected using corner tappings this may explain why Eq. 2.3
lies below the majority of the plotted data.
Nevertheless there is a large scatter in the plotted data, and so a single equation is
used to describe the effect of pipe roughness for all tappings. The equation used to
determine limits of pipe roughness is again taken from Eq. 2.2, but the A′ term is
included:
DCrough ¼ ð3:134 þ 4:726A0 Þb3:5 Dk
ð2:4Þ
It is not known whether the effect of change in friction factor increases for small
Reynolds number, but it is safer to include the term in A′ in calculating the limits of
pipe roughness. Moreover, there is little disadvantage in its inclusion since it causes
a slight reduction in the limits of pipe roughness in a range of Reynolds number
where they are already wide.
2.3 The Pipe
53
Shift in discharge coefficient, ΔC
0.035
Computed: Reader-Harris
Expt-Clark and Stephens
Expt-Herning and Lugt
Expt-Spencer et al
Expt-Thibessard
Expt-Witte
Expt-Bean and Murdock
Expt-Brennan et al
Expt-Studzinski et al
Eq. 2.5
0.030
0.025
0.020
0.015
0.010
0.005
0.000
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
β 3.5Δ λ
Fig. 2.15 The effect of rough pipe on the orifice plate discharge coefficient
In order to calculate the limits of pipe roughness for the discharge-coefficient
equation in ISO 5167-2:2003, it is necessary to use the measured values of relative
roughness for each pipe used to collect the data to obtain an approximate mean pipe
relative roughness for the data (and thus for the equation fitted to it). The mean pipe
relative roughness is a function of ReD: the estimates are given in Table 2.1.
k/D reduces with ReD because the higher Reynolds numbers generally occurred in
the larger pipes, which were generally relatively smoother. The values of friction
factor are consistent with the values of relative roughness if the Colebrook-White
Equation is used.
The maximum permissible shift in C depends on U, the stated uncertainty of
C. It is assumed here that the percentage shift, P, should not exceed the values in
Table 2.2.
Table 2.1 Values of k/D and λ associated with the Reader-Harris/Gallagher (1998) Equation
ReD
4
10 k/D
λ
104
3 × 104
105
3 × 105
106
3 × 106
107
3 × 107
108
1.75
0.031
1.45
0.024
1.15
0.0185
0.9
0.0155
0.7
0.013
0.55
0.0115
0.45
0.0105
0.35
0.010
0.25
0.0095
Table 2.2 Maximum
permissible percentage shift,
P, in C due to pipe roughness
P
β
0.5β
0.25
0.5(1.667β − 0.5)
1.13β3.5
β ≤ 0.5
0.5 < β ≤ 0.6
0.6 < β ≤ 0.71
0.71 < β
54
2 Orifice Design
This restriction ensures that for β ≤ 0.5, where other sources of error are
dominant, P/U < β; for 0.5 < β ≤ 0.71 P/U < 0.5; for 0.71 < β the maximum value of
P/U increases from 0.5 at β = 0.71 to 0.55 at β = 0.75.
Given the value of P in Table 2.2 and the value of λ associated with the data in
the database (and thus with the equation) in Table 2.1, it is possible from Eq. 2.4 to
calculate the maximum and minimum values of λ and hence of k/D for use with the
equation for each ReD and β. It was decided to write ISO 5167:2003 in terms of Ra
rather than k for specification of pipe roughness, since this is more convenient for
users, although k is still mentioned. The maximum and minimum values of Ra/D for
pipes upstream of orifice plates are given in Tables 1 and 2 of ISO 5167-2:2003.
It is stated in ISO 5167-2:2003 that the roughness requirements are satisfied in
both the following cases:
1 lm Ra 6 lm, D 150 mm, b 0:6 and ReD 5 107 :
1:5 lm Ra 6 lm, D 150 mm, b 0:6 and ReD 1:5 107 :
These are not additional restrictions, just a method of removing the need to use
Tables 1 and 2 of ISO 5167-2:2003 in some cases.
The tables prescribe k/D ≤ 0.005 even if the calculated value is higher. Although
the limits for very large ReD are much tighter than those in ISO 5167-1:1991, for
ReD = 3 × 105 they are very similar; this is unsurprising since the limits in ISO
5167-1:1991 were probably derived from data collected at around that Reynolds
number. The fact that the original orifice meters were not hydraulically smooth
means that in some situations a hydraulically smooth pipe is too smooth for the
Reader-Harris/Gallagher (1998) Equation to be used without additional uncertainty.
The minimum values for relative pipe roughness in Table 2 of ISO 5167-2:2003
represent exceedingly smooth pipes.
It might be argued that an equation with a friction factor term included explicitly
should have a lower uncertainty. Such an equation was rejected on the grounds that
it would be difficult to use.
2.3.3.2 Rough Pipes with a Smooth Portion Immediately Upstream
of the Orifice
The tests of Clark and Stephens (1957) included the effect of extremely rough pipes
(e.g. ones with peas stuck to them) and also the effect of cleaning: 5D of clean pipe
upstream of the orifice plate reduced the error due to roughness to about a tenth of
what it would have been. Where significant change in roughness over time might be
expected a possible strategy might be to use stainless steel pipe for the pipe
immediately upstream of the plate, carbon steel further upstream.
To examine the effect of a smooth section of pipe immediately upstream of an
orifice plate tests were undertaken at SwRI (Morrow et al. 2002) in a 4″ pipe.
2.3 The Pipe
55
Baseline data were taken with the whole upstream pipe of roughness Ra = 1.27 µm
(50 μin.). The pipe from 10D to 45D upstream of the orifice plate was then
roughened: the pipe roughness increased from 1.27 to 18.3 µm (50 to 719 μin.).
With β = 0.67 the results were very similar to the baseline (a shift in discharge
coefficient of 0.15 % in magnitude at most). This suggests that cleaning the last
10D of a pipe will in many cases be sufficient.
When two high-performance flow conditioners were included in turn
10D upstream of the orifice plate in the baseline pipe the data were very close to the
baseline; when the same flow conditioners were included in turn 10D upstream of
the orifice plate with roughened pipe from 10D to 45D upstream of the orifice plate
the data were again very close to the baseline. This suggests that rough pipe
upstream of a flow conditioner does not spoil its performance.
The final set of tests were carried out with the pipe rough [Ra = 18.3 µm
(719 μin.)] all the way from 45D upstream to the orifice plate: with β = 0.67 the
shift in discharge coefficient was an increase of about 1.7 %. Inserting the two highperformance flow conditioners in turn 10D upstream of the orifice plate with rough
pipe upstream and downstream of the flow conditioner gave a shift from the smooth
baseline at least as large as had been obtained with a rough pipe and no flow
conditioner and in some cases almost twice as large. So whereas rough pipe
upstream of the flow conditioner has very little effect, rough pipe downstream of the
flow conditioner may have a very significant effect.
2.3.3.3 Non-uniform Roughness
In practice roughness is often non-uniform, because in gas pipelines liquid is
particularly present on the bottom of the pipe. Before undertaking research in this
area video recordings of the inside of 10″ pipes (230 mm ID) were kindly lent to
NEL by BP Amoco, and from these it was concluded that it would not be unreasonable to assume that values of roughness height k of the order of 0.5 mm would
be possible. Accordingly experiments were undertaken with the same level of
relative roughness as had been found in these pipes (Reader-Harris et al. 2003).
To achieve the same relative roughness in a 4″ pipe as had been found by BP
Amoco gave k of the order of 0.2 mm. This corresponds to a P80 Sandpaper
(actually silicon carbide paper, commonly called wet and dry paper) with a grain
size of 197 μm. It was decided to work also with a smoother sandpaper (P240) with
a grain size of 60 μm. Sandpaper of each roughness was obtained and glued to the
inside of the pipe from ½D upstream of the orifice plate to 10D upstream of it. As
shown in Sect. 2.3.3.2 the discharge coefficient is largely affected by the pipe
roughness over the 10D upstream of the orifice plate, and it was necessary to leave
25 mm clean upstream of the flange tappings as the sandpaper was simply glued to
the surface. Flange Tappings D were at the bottom of the pipe (see Fig. 2.16) and
except where the whole pipe was rough the sandpaper was at the bottom of the pipe
and symmetrical about the bottom of the pipe. It was not simple to ensure that the
sandpaper remained stuck to the surface, but with the rougher sandpaper data were
56
2 Orifice Design
(a)
(b)
Flange Tappings C
Corner
Tappings
B
Corner
Tappings
A
Flange Tappings C
Corner
Tappings
B
(c)
Corner
Tappings
A
Flange Tappings D
Flange Tappings D
Flange Tappings C
Corner
Tappings
A
Corner
Tappings
B
Flange Tappings D
Fig. 2.16 Roughened portions of pipes relative to the pressure tappings. a Quarter pipe
roughened. b Half pipe roughened. c Whole pipe roughened
obtained in which the sandpaper remained satisfactorily stuck to the walls. The
smoother sandpaper was generally weaker, and so in addition to its tendency to
become unstuck it also became wavy in use, and no satisfactory data could be
obtained.
The data obtained with the rougher sandpaper are presented in Fig. 2.17. It is
interesting that similar data are obtained with each pair of tappings and that the shift
is approximately proportional to the fraction of the pipe which is rough. According
to Eq. 2.3 for uniformly rough pipe the predicted shift in discharge coefficient at
ReD = 2.74 × 105 was 1.26 %, using the Colebrook-White Equation (Eq. 1.21) to
determine the friction factor and assuming that the smooth pipe had Ra = 0.8 μm
and that k = πRa. Additionally it would be expected that for entirely rough pipe the
thickness of the roughness elements and the paper might increase the shift in
discharge coefficient by 0.4 %. So the measured shift in discharge coefficient of
1.98 % compares quite well with the predicted value of 1.66 %.
% shift in discharge coefficient
2.5
2.0
Corner Tappings A
Corner Tappings B
Flange Tappings C
1.5
Flange Tappings D
Mean Tappings
1.0
0.5
0.0
Quarter upstream
pipe rough
Half upstream
pipe rough
Entire upstream
pipe rough
Fig. 2.17 % shift in discharge coefficient due to rough pipe upstream of an orifice plate (β = 0.67)
2.3 The Pipe
57
2.3.4 Steps and Misalignment
Over the first 2D of the pipe upstream of the orifice no measured diameter of the
pipe is permitted to differ by more than 0.3 % from D, the mean diameter of the
pipe (see 6.4.2 of ISO 5167-2:2003 and Sect. 2.4). To be consistent with ISO 51672:2003 a protruding weld should not cause a change in measured diameter greater
than 0.3 %; if it is greater than this value the weld bead should be removed.
The basis on which this requirement was derived is not clear, but Teyssandier
(1985) considered the effect of steps or gaps D/4 wide adjacent to an orifice plate or
2D upstream of it in a 2″ pipe. As far as these data are concerned a limit of 0.3 % in
maximum permissible step as in ISO 5167-2:2003 appears conservative.
Beyond 2D from the orifice the standard is less clear. The rules on steps are
clear, if rather complicated. They result from NEL tests (Reader-Harris and Brunton
2002): Fig. 2.18 shows the shift in discharge coefficient where pipes of different
schedule were placed at different distances upstream of a schedule 40 pipe: the
effect of a contraction by about 5 % of D (Schedule 10 to Schedule 40) is much less
than the effect of an expansion by about 5 % of D (Schedule 80 to Schedule 40).
The data point for a Schedule 40 pipe shown in the figure was taken using an
ordinary Schedule 40 pipe, whereas the baseline pipe was honed. 6.4.3 of ISO
5167-2:2003 permits steps of up to 0.3 % of D beyond 2D from the orifice plate and
up to 2 % of D beyond 10D from the orifice plate. If the step is a contraction it
permits steps of up to 6 % of D beyond 10D from the orifice plate. It also permits
steps (expansions or, of course, contractions) of up to 6 % of D beyond the closest
permissible location for the insertion of an expander provided that the step is also at
0.6
% shift in discharge coefficent
0.5
0.4
Schedule 10
0.3
Schedule 40
0.2
Schedule 80
Schedule 120
0.1
0.0
-0.1
-0.2
-0.3
-0.4
0
10
20
30
40
50
Diameters from orifice plate
Fig. 2.18 Upstream steps: % shift in discharge coefficient due to pipes at various distances
upstream of an orifice plate (β = 0.67) in a Schedule 40 pipe (Reader-Harris and Brunton 2002)
58
2 Orifice Design
least 10D from the orifice plate. Although larger steps could be used satisfactorily
for sufficiently small β it is generally wise to design a system so that β may be easily
changed if the flow is higher or lower than the design flow.
The aim of these changes to ISO 5167 was to avoid the requirement to use
machined pipes beyond 10D from the orifice. Moreover, a change of 6 % of
D generally permits a change from one common pipe schedule to the next. The
NEL tests provide justification for common practice in calibration laboratories
where upstream pipes of the same nominal diameter but larger internal diameter
than the customer’s meter are used 25D, say, upstream of the meter.
The steps in Reader-Harris and Brunton (2002) were concentric steps, but at steps
there may be offsets as well: 6.4.3 of ISO 5167-2:2003 states that the actual step
caused by misalignment and/or change in diameter shall not exceed the permitted
diameter step at any point of the circumference. To meet these restrictions will
probably require the use of dowels or the equivalent to ensure alignment. If it is
intended to machine the pipe immediately upstream of the orifice plate but not to
machine the pipe upstream of that then the latter pipe should be selected to be
sufficiently cylindrical that the former pipe can be machined to a diameter such that
where the flanges meet there is a sufficiently small step. If the pipe immediately
upstream of the orifice plate is manufactured first then the pipe upstream of that may
require machining, and it may be necessary to buy a thicker walled pipe to machine.
What is not clear are the rules where the internal diameter of the upstream pipe
changes not suddenly (as with a step) but gradually. This is not permitted in the first
2D upstream of the orifice plate. If the diameter change occurs more than 2D away
it is not clear what is permitted. The standard is not clear because of a lack of
experimental data. What often results in poor practice is to buy a pipe for installation immediately upstream of the orifice, measure it, find it insufficiently cylindrical, machine the first 2D until it is sufficiently cylindrical, and then blend the
machined and unmachined diameters at 2D. The problem with this is that it leaves
an expansion 2D upstream of the orifice. It is much better to work the other way
round, i.e. to start with an upstream pipe a little shorter than is required, to weld a
piece of thicker-walled pipe to the upstream pipe (the thicker-walled pipe is to be
adjacent to the orifice plate) and to machine the thicker-walled pipe so that it
approximately matches the rest of the upstream pipe and there is very small
deviation from constant diameter and concentricity where the machined and unmachined sections are blended. For 2″ orifice meters it is reasonable to machine the
whole upstream length; for 24″ meters it is desirable either to select the pipework so
that no machining is required or to have it manufactured to the required tolerance;
for 8″ meters machining of a part of the upstream length is probably required.
Goodson et al. (2004) studied the effect of recesses corresponding to those
formed where an RTJ-flanged orifice fitting is joined to an upstream meter tube:
tests in 4″ (β = 0.2, 0.4 and 0.67) and 8″ (β = 0.67) showed that the effect of the
recesses was negligible.
If gaskets (rather than ‘O’ rings) are used between pipes or at the orifice it is
important that they do not protrude into the pipe; therefore, in practice there will be
a small recess. 5.2.6.6 of ISO/TR 9464:2008 recommends that at the plate a gasket
2.3 The Pipe
59
be not thicker than 0.03D; such a gasket will have a negligible effect on the
discharge coefficient.
Straightness of the upstream pipe is defined by 7.1.3 of ISO 5167-1:2003, and is
normally checked visually.
The downstream pipe diameter is much less critical: 6.4.6 of ISO 5167-2:2003
states that it only needs to be within 3 % of that of the upstream pipe: Teyssandier
(1985), using a 2″ orifice meter with flange tappings, looked at the effect of a
protrusion or a recess D/4 wide at the orifice plate on its downstream side and found
that for β = 0.3 or 0.5 its effect is less in magnitude than 0.1 % for protrusions or
recesses up to 0.0625D in height (or depth) and less in magnitude than 0.2 % for
protrusions or recesses up to 0.125D in height (or depth); for β = 0.7 its effect is less
in magnitude than 0.1 % for a protrusion up to 0.03125D in height or a recess up to
0.0625D in depth. From those data it can be seen that provided that a protrusion is
less than 20 % of the dam height its effect is less than 0.1 %; it is not surprising that
the effect increases rapidly when the protrusion is a large percentage of the dam
height (at 83 % of the dam height for β = 0.7 the effect is 5.25 %); at 100 % of the
dam height a thick plate is obtained. The dam height is the distance from the sharp
edge of the orifice plate to the nearest point of the pipe wall, i.e. Dð1bÞ
2 . Teyssandier
(1985) also looked at the effect of a protrusion or a recess D/4 wide 2D downstream
of the orifice plate and found that even a protrusion 0.125D in height for β = 0.7 had
an effect of only 0.1 %.
In conclusion, the rules on steps are given in 6.4 of ISO 5167-2:2003. They are
rather complicated; an explanation for much of their complexity has been given in
this section.
2.3.5 Eccentricity
The orifice plate and the pipe need to be close to concentric. The effect of eccentricity has been measured by Norman et al. (1984), Husain and Teyssandier (1986a)
and Miller and Kneisel (1968). The eccentricity (i.e. the distance between the
centre-line of the pipe and that of the orifice) is generally non-dimensionalized with
D/(0.1 + 2.3β4). This non-dimensionalization was used in ISO 5167:1980 (ISO
1980). When an orifice plate with a single tapping upstream and downstream is
used the effect of eccentricity is greater in the direction parallel to the tappings than
in the direction perpendicular to them. The limit on eccentricity in ISO 5167-2:2003
parallel to the tappings is
0:0025D
0:1 þ 2:3b4
and that in the direction perpendicular to the tappings is twice that.
ð2:5Þ
60
2 Orifice Design
NOTE The limit in ISO 5167:1980 was 0.0005D/(0.1 + 2.3β4) in all directions. In
ISO 5167-1:1991 (ISO 1991) it was increased to 0.0025D/(0.1 + 2.3β4) in all
directions. In ISO 5167-2:2003 it remained unchanged parallel to the tappings but
was increased perpendicular to the tappings.
In 2.6.2.1 of API MPMS 14.3.2 the same limit as in Eq. 2.5 is applied parallel to the
pressure tappings, but in the direction perpendicular to the pressure tappings the
limit is four times that in Eq. 2.5. The ISO limit according to Fig. 6 of ISO/TR
12767:2007 gives shifts in the perpendicular direction up to about 0.08 % in
magnitude, the API up to about 0.15 %. API MPMS 14.3.2 allows twice as large a
limit if tappings 180° apart are connected; however, Fig. 6 of ISO/TR 12767:2007
shows that sometimes there is no cancellation. The ISO limits appear reasonable.
If the eccentricity is close to the limit, determining whether the eccentricity is
inside or outside the limit is not trivial: if the plate is held between three dowels the
deviation between the centreline of the orifice and that of the outside of the orifice
plate, the deviation between the centreline of the pipe and the centre of the circle
formed by the inside of the dowels, and the possible variation in the location of the
plate within the dowels will all have to be considered.
On one occasion an orifice plate was installed so eccentrically that there
was flow past the outside of the plate: this problem was investigated by Barton
et al. (2005).
According to 6.5.2 of ISO 5167-2:2003 the plate shall be perpendicular to the
pipe centreline within 1°. Whether this is based on engineering judgment or on
experiment is not clear. This requirement should be stated when specifying alignment of flanges being welded during fabrication.
2.4 Dimensional Measurements
Where an orifice plate is being used without flow calibration the dimensional
measurements are crucial to the calculated flowrate. The value for orifice diameter
used in Eq. 1.15 is the mean of at least four measurements of diameter in different
orientations (5.1.8.2 of ISO 5167-2:2003). 6.4.2 of ISO 5167-2:2003 requires that
at least four measurements of diameter be made in each of three planes in the pipe.
ISO 5167-2:2003 gives limits on the variation in diameters permitted, but measured
uncertainties lower than the maximum permitted in ISO 5167-2:2003 can be used in
the uncertainty of the mass flowrate (see Sect. 4.8). Modern coordinate measuring
machines often do not give individual diameters but give a mean diameter and
circularity; nevertheless, it can easily be checked whether the measurements meet
the intention of ISO 5167-2:2003. For the pipe the mean diameter is obtained from
the average of measurements made in at least three planes over a distance of
0.5D upstream of the upstream pressure tapping: one plane must be at 0D, one at
0.5D, from the upstream tapping and one in the plane of the weld in the case of a
weldneck construction.
2.4 Dimensional Measurements
61
The measurements of the orifice are considerably more important than those of
the upstream pipe (see Eq. 4.13 in Sect. 4.8): no orifice diameter may differ by more
than 0.05 % from the mean, whereas in the pipe the tolerance is 0.3 %. In practice
this is a minimum requirement. One of the advantages of orifice metering is that the
diameter in the discharge-coefficient equation is that of the orifice plate. Where β is
small a low quality pipe is acceptable, provided that the orifice plate is of high
quality. For larger β the effect of any error in pipe diameter becomes more significant: from Eq. 4.13 the effect can be approximately calculated.
2.5 Orifice Fittings
The orifice fitting, which enables the operator to change or remove an orifice plate
easily (i.e. without undoing flange bolts), was introduced by Paul Daniel. Tests
were undertaken in 1949–51 in Rockville by the joint AGA-ASME committee to
compare measurement uncertainty using orifice fittings with that obtained using
plates held between flanges (AGA 1951, 1954a). Tests were also carried out as part
of the Refugio tests in 1952/3: an orifice plate held between flanges (an orifice
flange union) and an orifice fitting were placed in a 30″ line, the former upstream of
the eight 10″ reference meters and the latter downstream, and ‘it was unanimously
concluded that the equations for computing coefficients of discharge in AGA Gas
Measurement Report No 2 may be used, within the tolerances given, for large
diameter meter tubes (e.g., 30-in.) using either orifice flange unions or orifice
fittings’ (AGA 1954b).
A picture of an orifice plate emerging from an orifice fitting is shown as
Fig. 2.19.
Some systems are designed so that an orifice plate may be changed without
depressurizing the line.
Fig. 2.19 Orifice plate
emerging from an orifice
fitting
62
2 Orifice Design
2.6 Pressure Loss
The pressure loss is required for hydraulic system design, but a more accurate value
is required if the pressure loss ratio (the ratio of the pressure loss to the differential
pressure) is to be used for diagnostic purposes (see Sect. 4.10).
The pressure loss for an orifice plate is calculated as follows. The reader is
warned that this section is more mathematically complex than the rest of the book.
The momentum theorem is obtained by integrating the equation of motion over a
fixed volume so that
q
Dui
@rij
¼ qFi þ
;
Dt
@xj
ð2:6Þ
where ρ is the density, ui the velocity in the xi-direction, Fi the body force, σij the
stress tensor and D/Dt the derivative following the motion of the fluid, becomes, on
expanding the derivative following the motion of the fluid and using mass conservation and the divergence theorem,
ZZZ
V
ZZ
ZZZ
ZZ
@ðui qÞ
dV ¼ qui uj nj dA þ
Fi qdV þ
rij nj dA
@t
A
V
ð2:7Þ
A
where the fixed volume V is bounded by surface A.
The stress tensor consists of two terms: the pressure term is sufficient for the
approximation here, so σij = −pδij. The flow is steady and the body force (gravity)
makes a contribution to the pressure which will make no contribution to the
pressure loss.
Equation 2.7 is applied to the volume marked V on Fig. 2.20. Equations are
supplied for incompressible flow.
p1
p3
V
p2
orifice plate
Fig. 2.20 Pressures during flow through an orifice plate
2.6 Pressure Loss
63
Then, assuming that the pressure has the same value on the back of the orifice
plate, on the edge of the orifice jet as far as the vena contracta (i.e. the point of
maximum convergence) and at the vena contracta, and using the divergence theorem
0 ¼ qAc u2c qAp u2p p3 Ap þ p2 Ap
ð2:8Þ
where Ac and Ap are the area of the vena contracta and of the pipe, respectively,
c and u
up are the mean velocity in the vena contracta and in the pipe, respectively,
and p2 and p3 are the pressure immediately downstream of the orifice (e.g. at a
downstream pressure tapping) and after pressure recovery, respectively.
In addition Bernoulli’s Equation (see Sect. 1.3) applies between an appropriate
location upstream of the orifice plate and the vena contracta:
1
1
p1 þ qu2p ¼ p2 þ qu2c
2
2
ð2:9Þ
where p1 is the pressure around 1D upstream of the orifice.
The basic equation for differential-pressure meters (Eq. 1.15, for incompressible
flow) can be expressed as:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C
2ðp1 p2 Þ
uo ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi
ð2:10Þ
4
q
1b
where uo is the mean velocity in the orifice. Mass conservation between upstream of
the orifice plate, the orifice and the vena contracta gives:
qup Ap ¼ quo b2 Ap ¼ quc Ac :
ð2:11Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 b4 ð1 C 2 Þ Cb2
D- p1 p3
¼
¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
;
Dp p1 p2
1 b4 ð1 C 2 Þ þ Cb2
ð2:12Þ
Equations 2.8–2.11 give
where D- is the pressure loss (from D upstream to 6D downstream).
Of the three standard tapping pairs D and D/2 tappings are the most suitable for
determining C for use in Eq. 2.12.
Equation 2.12 is given as Eq. (7) in 5.4.1 of ISO 5167-2:2003. The inclusion of
this equation in ISO 5167 resulted from the publication of Urner (1997).
A simpler but less accurate approximation is
D¼ 1 b1:9 ;
Dp
which is given in 5.4.2 of ISO 5167-2:2003.
ð2:13Þ
64
2 Orifice Design
Equation 2.12 has been checked by looking at data from Steven et al. (2007).
Strictly speaking Eq. 2.12 is applicable to the situation where the upstream tapping
is at D upstream. Since Steven’s tappings were in the flanges his measured pressure
Dloss ratio Dpupup was not equal to the true pressure loss ratio DDp .
The measured pressure loss ratio
D-up
Dpup ,
where the upstream tapping is a flange or a
corner tapping, is related to the true pressure loss ratio
D-
DDp
by
pup p1
D-up pup p3 Dp þ p1 p2
¼
¼
p p
Dpup pup p2
1 þ pup1 p21
ð2:14Þ
where pup is the pressure at the upstream pressure tapping. It is not easy, given the
assumptions in the use of the momentum theorem, to include a term for the location
of the downstream flow-measurement tapping: its effect is small and neglected in
Eq. 2.14.
Moreover, from Eq. 1.15,
pup p1 þ 2
CDD=2 CupD=2
ðp1 p2 Þ
CDD=2
ð2:15Þ
where the difference in discharge coefficient between that for a plate with tappings
D upstream and D/2 downstream, CD-D/2, and that for a plate with tappings at a
different upstream location and D/2 downstream, Cup-D/2, can be obtained from the
Reader-Harris/Gallagher (1998) Equation (see Eq. 5.22).
So,
CDD=2 CupD=2
pup p1
2
p1 p2
CDD=2
ð2:16Þ
Then the measured pressure loss ratio in Steven et al. (2007) can be compared with
calculated values of the pressure loss ratio, obtained by substituting Eqs. 2.12 and
2.16 into Eq. 2.14: see Fig. 2.21. The equation in 2.4.5.1 of API MPMS
14.3.2:2000 is also shown.
It appears possible to predict pressure loss remarkably accurately, but the population of data is very small.
The formula for pressure loss applies where the downstream pressure loss tapping is about 6D downstream of the orifice plate, where the pressure has recovered
(to the maximum extent that it does recover). No term for friction loss has been
included: it might be appropriate to include one, but, where the upstream and
downstream tappings are 1D and 6D respectively from the orifice plate, the friction
loss will be significantly less than the friction loss in fully developed flow through
7D of straight pipe.
2.6 Pressure Loss
65
% deviation of calculated value from
measured value
5
4
3
2
1
0
-1
2.4.5.1 of API 14.3.2:2000
-2
5.4.1 of ISO 5167-2:2003
-3
5.4.2 of ISO 5167-2:2003
Eqs 2.12, 2.14 and 2.16
-4
-5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
β
Fig. 2.21 Pressure loss ratio: deviation of calculated values from measured CEESI data (taken in
dry gas for their wet-gas JIP): only ‘Eqs. 2.12, 2.14 and 2.16’ takes specific account of the
upstream tapping location
In conclusion, Eq. (7) in ISO 5167-2:2003 for pressure loss ratio (Eq. 2.12)
appears remarkably accurate: if the upstream tapping is not located 1D upstream of
the orifice plate and the pressure loss ratio that will actually be measured is
required, the necessary additional term has been derived.
2.7 Reversed Orifice Plates
The effect of reversing an orifice plate is very large. An increase in discharge
coefficient of the order of 15 or 20 % is typical. Much of the published literature
relating to the discharge coefficients of reversed orifice plates has notable deficiencies when considered for general application. In most papers the orifice plates
are not fully described: some papers do not give the bevel angle, and the size of the
bevel is rarely stated.
8.6.2 of ISO/TR 12767:2007 (ISO 2007c) provides information on the variation
of discharge coefficient with bevel size. However, as no orifice diameter is given,
the data cannot be used to determine the magnitude of error in a specific case of
interest. 6.1 of ISO/TR 15377:2007 (ISO 2007b) describes the ‘conical entrance’
orifice, which is considered to have a constant discharge coefficient of 0.734.
However, the conical entrance orifice is not sufficiently representative of reversed
square-edged orifice plates to give results of general application. In SPE Note
22867 (Ting 1991) the author describes the results of a number of tests with air at
66
2 Orifice Design
low Reynolds numbers. The tests were carried out for various β, but neither bevel
angle nor bevel size is given in the paper. When consulted, the author stated that he
believed that the bevel angle was 30° to the face of the plate.
Witte (1997) published a paper on the effect of reversing orifice plates in a 10″
pipe in gas at 60 barg. The plates had thickness, E, of 6.35 mm (¼″) with 45° bevel.
The orifice (bore) thickness, e, was 4.76 mm (3=16″), although this is not stated in the
paper. Witte carried out the work at the Gas Research Institute Metering Research
Facility at Southwest Research Institute. Morrow (2000) reanalysed Witte’s data.
CFD was undertaken by Brown et al. (2000). Morrow also measured the effect of
reversing a series of plates in a 4″ line; these plates had a bevel angle of 45°, a plate
thickness, E, of 3.18 mm (1=8″) and an orifice (bore) thickness, e, of 1.59 mm (1=16″).
George and Morrow presented the data listed above and both 2″ data and additional
4″ data and presented conclusions in George and Morrow (2001).
Even where the bevel angle is 45° no simple formula has achieved universal
acceptance. The correlation in George and Morrow (2001), also quoted in Morrow
et al. (2002), is
% flowrate error ¼ 18:93 þ 12:91b 34:04
e 2
E
e
8:900 þ 13:64
Dnom
E
E
ð2:17Þ
This does not have the correct performance in the limit as b/E tends to 0, where b is
the bevel width (=E − e), (i.e. e/E tends to 1).
The error should be a function of b/d (similar to edge rounding), but not of
b/d alone: β is significant too. Figure 2.22 shows the experimental data for bevel
angle 45° from SwRI including those of Witte plus two points from NEL. The lines
described as ‘experiment’ join up the experimental data for each value of β. If the
bevel is treated as a rounded edge and the best-fit radius determined as in
Sect. 2.2.4, then the best–fit radius is 1.57b (presumably πb/2). Then the expected
flowrate error for a bevelled edge can be calculated as in Sect. 2.2.4. This has been
plotted for a maximum ratio of edge radius to diameter of 0.01, since the data of
Burgin (1971) show that above that value the data deviate increasingly from the fit
in Sect. 2.2.4.
The data from Witte appear different (especially for β = 0.2) from the other data
sets. This could be due to e/E being equal to 0.75. So the other data points (i.e.
those for e/E ≤ 0.5) in Fig. 2.22 were fitted with the following equation:
% flowrate error ¼ ða bbc Þ
This behaves correctly as b/d tends to 0.
f db
1 exp
a bbc
2.7 Reversed Orifice Plates
0
MRF: 2 inch: e/E = 0.25
George and Morrow: 4 inch: e/E < 0.25
NEL: 8 inch: e/E = 0.5
Experiment: beta = 0.2
Experiment: beta = 0.5
Experiment: beta = 0.67
Rounded edge: radius = 1.57b
Eq. 2.18: beta = 0.4
Eq. 2.18: beta = 0.6
Eq. 2.18: beta = 0.75
-2
% error in measured flowrate
67
-4
-6
MRF: 4 inch: e/E = 0.5
George and Morrow: 4 inch: e/E = 0.5
Witte: 10 inch: e/E = 0.75
Experiment: beta = 0.4
Experiment: beta = 0.6
Experiment: beta = 0.75
Eq. 2.18: beta = 0.2
Eq. 2.18: beta = 0.5
Eq. 2.18: beta = 0.67
-8
-10
-12
-14
-16
-18
-20
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
b /d
Fig. 2.22 Error in measured flowrate using a reversed orifice plate
With the fit
% flowrate error ¼ 17:2 10:4b2:5
1 exp
1270 db
17:2 10:4b2:5
ð2:18Þ
the r.m.s. deviation of the equation from the data is 0.35 %. Equation 2.18 is shown
on Fig. 2.22.
To avoid having a problem with a reversed plate, where possible a plate should
be marked externally in such a way that correct orientation can be verified without
looking into the pipe.
2.8 Conclusions
This chapter has described the main design specifications for orifice plates: it has
pointed the reader to important parts of ISO 5167 and given reasons for the
requirements in the standard. It has covered the orifice plate (the circularity of
the bore, the flatness, the parallelism of the two faces, the surface condition of the
upstream face, and, above all, the edge sharpness), the pipe (the pressure tappings,
the pipe roughness, the effect of upstream steps, the concentricity of the orifice plate
in the pipe and the circularity and cylindricality of the pipe), the measurements of
both the orifice plate and the pipe, and the pressure loss. A very significant incorrect
installation of an orifice plate within the pipe, a reversed orifice plate, has also been
68
2 Orifice Design
covered. Appendix 2.A considers the use of orifice plates of diameter smaller than
that permitted in ISO 5167-2:2003.
The basic instruction remains to follow ISO 5167. For some important deviations from ISO 5167 the errors in discharge coefficient can be calculated using what
is described in this chapter.
Appendix 2.A: Orifice Plates of Small Orifice Diameter
2.A.1 Introduction and Test Work
Orifice plates of small orifice diameter, d, are often used for measuring low gas
flowrates in declining wells in order to increase the available differential pressure.
However, some flowrates may result in the orifice diameter being sufficiently small
that the orifice diameter is outside ISO 5167-2:2003, i.e. less than 12.5 mm
(0.492″).
Twelve orifice plates were obtained and tested by NEL for ConocoPhillips, four
of them from a manufacturer that specializes in spark erosion techniques, eight of
them from a manufacturer that specializes in orifice plates. The aim was to determine the probable errors that might be obtained in using orifice plates of very small
sizes.
Accordingly four orifice plates were manufactured for the project by ATM
(Advanced Tool Manufacture), East Kilbride, Scotland and used electrical discharge machining (EDM—or spark erosion) to machine the orifice bore; eight were
manufactured by Kelley Orifice Plates, Texarkana, Texas using conventional
machining techniques. From ATM, the orifice diameters were 6.35 mm (1=4″),
3.18 mm (1=8″) (2 off) and 1.59 mm (1=16″); from Kelley they were 9.52 mm (3=8″),
6.35 mm (1=4″), 3.18 mm (1=8″) and 1.59 mm (1=16″) (2 off in each case). In the case
of ATM e/d = 0.1 was specified, where e is the thickness of the orifice, and d the
orifice diameter (see Sect. 2.2.5).
All the orifice plates were calibrated in water in a 4″ line (D = 101.80 mm) over a
range of Reynolds number. The Reynolds number was below the minimum pipe
Reynolds number of 5000 permitted by ISO 5167-2:2003 for all the data, except for
most of the d = 9.52 mm (3=8″) data. The data are shown in Reader-Harris et al.
(2008). The smallest value of pipe Reynolds number was 116; so the deviations
here are presented from the complete orifice plate discharge-coefficient equation:
Appendix 2.A: Orifice Plates of Small Orifice Diameter
69
C ¼ 0:5961 þ 0:0261b2 0:216b8 þ 0:000521 ð106 b=ReD Þ0:7
þ ð0:0188 þ 0:0063AÞb3:5 maxfð106 =ReD Þ0:3 ; 22:7 4700 ðReD =106 Þg
þ ð0:043 þ 0:080 e10L1 0:123 e7L1 Þð1 0:11AÞ
0
b4
1 b4
0
0:031 ðM2 0:8M21:1 Þf1 þ 8maxðlg ð3700=ReD Þ; 0:0Þgb1:3
ð5:21Þ
þ 0:011 ð0:75 bÞmaxð2:8 D=25:4; 0:0Þ
where D is the pipe diameter in mm (following ISO 80000-2:2009, log10 is written lg).
The Reader-Harris/Gallagher (1998) Equation in ISO 5167-2:2003 (ISO 2003b)
(given here as Eq. 5.22) is the special case of Eq. 5.21 for ReD ≥ 5000. The
differences between Eq. 5.21 and the extrapolated Reader-Harris/Gallagher (1998)
Equation are very small, less than 0.06 % in magnitude, over the range of the data
here.
For each orifice plate the mean deviation of the data from Eq. 5.21 over its range
of Reynolds number is given in Fig. 2.A.1: the mean deviations are plotted against
orifice diameter. To use a simple additive correction to Eq. 5.21 for each orifice
plate it is necessary that the deviation be almost constant over its range of Reynolds
number: for each orifice plate the standard deviation of the deviations from Eq. 5.21
over its range of Reynolds number is given in Fig. 2.A.2.
Mean % shift in discharge coefficent
7.0
ATM
Kelley
6.0
5.0
4.0
3.0
2.0
1.0
0.0
-1.0
0
2
4
6
8
10
12
d (mm)
Fig. 2.A.1 Mean percentage shift in discharge coefficient from Eq. 5.21 for each orifice plate over
its range of Reynolds number
70
2 Orifice Design
Standard deviation of % shift
1.20
1.00
0.80
ATM
Kelley
0.60
0.40
0.20
0.00
0
2
4
6
8
10
12
d (mm)
Fig. 2.A.2 Standard deviation of percentage shift in discharge coefficient from Eq. 5.21 for each
orifice plate over its range of Reynolds number
From Fig. 2.A.2 for all the ATM data and for most of the Kelley data the
deviation from Eq. 5.21 (and hence from the Reader-Harris/Gallagher (1998)
Equation) was fairly constant and so Eq. 5.21 could be used with a simple additive
correction, presumably due to edge rounding. The fact that there appears to be a
simple rounding correction for most of the sets supports the view that, given such
an edge-rounding term, Eq. 5.21 can be used with general success for orifice plates
that have both small d and small β.
If the orifice plates calibrated here were to be used in service they would be used
with a simple additive shift as given in Fig. 2.A.1. Since, however, they were a
sample of plates used to determine how other plates from the same manufacturers
would perform in service then further analysis was necessary.
If the edge radius of an orifice plate is r, and the increase in edge radius is Δr, the
percentage increase in discharge coefficient, S, is given by Hobbs and Humphreys
(1990) (see Sect. 2.2.4):
S ¼ 550
Dr
:
d
ð2:A:1Þ
So given a shift in discharge coefficient it is possible to calculate the increase in
edge radius that gives rise to it. It is not clear on what relative edge radius Eq. 5.21
is based at the low throat Reynolds numbers obtained with these plates. If it were
Appendix 2.A: Orifice Plates of Small Orifice Diameter
71
25
20
r (μm)
15
ATM
Kelley
10
5
0
-5
0
2
4
6
8
10
12
d (mm)
Fig. 2.A.3 Calculated edge radius of orifice plates v d
assumed that it is based on r/d = 0.0004, that is the maximum permitted edge radius
in ISO 5167-2:2003 (at high Reynolds numbers with larger plates Eq. 5.21 (and
thus the Reader-Harris/Gallagher (1998) Equation) is based on relatively sharper
plates), then the edge radii for the different plates would be as shown in Fig. 2.A.3.
The mean edge radius of the ATM plates is calculated to be 8.7 µm.
NOTE If the PR 14 Equation (Eq. 5.C.2) were used instead of Eq. 5.21 the mean
edge radius of the ATM plates would be calculated to be 10.9 μm. If Eq. 5.21 were
used but it were assumed that at these low throat Reynolds numbers Eq. 5.21 was
based on r/d = 0.0003 the mean edge radius of the ATM plates would be calculated
to be 0.36 μm smaller than if Eq. 5.21 were based on r/d = 0.0004.
When the following term (based on an edge radius of 8.7 μm and Eq. 2.A.1) is used
DC ¼ 3:3
0:0087
0:0004 ðd : mmÞ
d
ð2:A:2Þ
95 % of the ATM data lie within 0.65 % of Eq. 5.21 with term 2.A.2 added.
In Fig. 2.A.4 the data from the spark-eroded plates are compared with Eq. 5.21
(essentially the Reader-Harris/Gallagher (1998) Equation) with an additional term
representing an edge radius of 8.7 μm.
The Stolz Equation in ISO 5167:1980 (ISO 1980) (given here as Eq. 5.24) does
not give good performance as β tends to 0.
It is more difficult to analyse the data from the Kelley plates: the analysis is
provided in Reader-Harris et al. (2008).
72
2 Orifice Design
0.635
d = 1.577 mm (1/16")
d = 3.157 mm (1/8")
d = 3.169 mm (1/8")
d = 6.32 mm (1/4")
Eq. 5.21: beta = 0, D > 71.12 mm
Eq. 5.21 with term 2.A.2 added: d = 1.577 mm
Eq. 5.21 with term 2.A.2 added: d = 3.157 mm or 3.169 mm
Eq. 5.21 with term 2.A.2 added: d = 6.32 mm
Stolz Equation
0.630
Discharge coefficient, C
0.625
0.620
0.615
0.610
0.605
0.600
0.595
0.590
0
5
10
15
20
25
30
35
(106/Red ) 0.7
Fig. 2.A.4 The discharge-coefficient data from the spark-eroded orifice plates
2.A.2 Conclusions
Orifice plates can be a surprisingly good way of measuring small gas flows. The
Reader-Harris/Gallagher Equation appears to work well for small orifices if an
additional term is added to allow for edge rounding (from Sect. 2.2.5 it would be
wise also to specify that e/d ≤ 0.1). The edge radius for the spark-eroded plates
appears to be fairly constant as d decreases, and so for uncalibrated spark-eroded
orifice plates from one manufacturer good results may be obtained by adding term
2.A.2 arithmetically to the Reader-Harris/Gallagher (1998) Equation. Results presumably depend on the manufacturer. An orifice plate with edge radius equal to the
average edge radius of the plates manufactured by ATM will meet the requirements
of ISO 5167-2:2003 provided that d is greater than 22 mm. On this basis in a 24″
line an orifice plate with β = 0.05 would still have a sharp edge and not require an
additional term added to the discharge-coefficient equation.
To be able to use orifice plates of very small orifice diameter in an existing
installation in a declining gas field may be much more economical than to replace
the metering or shut the field. From the beginning of the flow measurement to its
conclusion a 4″ orifice meter with different orifice plates (including those described
in this appendix) might measure a range of around 3000:1 in terms of mass flowrate
(if the static pressure were the same throughout the period of measurement).
References
73
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